An ideal gas has the following initial conditions: Vi = 490 cm3, Pi = 5 atm, and Ti = 100°C. What is its final temperature if the pressure is reduced to 1 atm and the volume expands to 1000 cm3?
_____°C
P1V1/t1=P2V2/T2
T2=P2V2/(p1V1)* T1
change t1 to degrees K, NOT C.
To solve this problem, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = gas constant
T = temperature
The gas constant, R, has a value of 0.0821 L•atm/mol•K.
First, we need to find the number of moles of the gas using the initial conditions.
We can use the equation:
n = (Pi * Vi) / (R * Ti)
Substituting the given values:
n = (5 atm * 490 cm3) / (0.0821 L•atm/mol•K * (100°C + 273.15))
Note that we need to convert the volume from cm3 to L and the temperature from °C to Kelvin.
Next, we can use the ideal gas law equation to find the final temperature:
Tf = (Pf * Vf) / (n * R)
Substituting the given values:
Tf = (1 atm * 1000 cm3) / (n * 0.0821 L•atm/mol•K)
Finally, we can substitute the value of n we calculated earlier to find the final temperature:
Tf = (1 atm * 1000 cm3) / ((Pi * Vi) / (R * Ti) * 0.0821 L•atm/mol•K)
Simplifying this expression will give us the final temperature. Let's calculate it:
Tf = (1 atm * 1000 cm3 * R * Ti) / (Pi * Vi)
Using the given values:
Tf = (1 atm * 1000 cm3 * 0.0821 L•atm/mol•K * (100°C + 273.15)) / (5 atm * 490 cm3)
Calculating this expression will give us the final temperature:
Tf ≈ 670.3°C
Therefore, the final temperature is approximately 670.3°C.